College Algebra 9th txtbk

272 CHAPTER 4 POLYNOMIAL AND RATIONAL FUNCTIONS
Technology Connections
Figure 8 shows the details of constructing the cubic model
of Example 9 on a graphing calculator.
1,000
0
70
Z Figure 8
(a) Entering the data
(b) Finding the model
0
(c) Graphing the data and the model
MATCHED PROBLEM 9 Use the cubic model of Example 9.
(A) Estimate the weight of a sturgeon of length 65 inches.
(B) Compare the weight of a sturgeon of length 30 inches as given by Table 1 with the
weight given by the model.
EXAMPLE 10
Table 2
U.S. Consumption of
Hydroelectric Power
Year (Quadrillion BTU)
1983 3.90
1985 3.40
1987 3.12
1989 2.99
1991 3.14
1993 3.13
1995 3.48
1997 3.88
1999 3.47
2001 2.38
2003 2.53
2005 2.61
Source: U.S. Department of Energy
SOLUTIONS
Hydroelectric Power
The data in Table 2 gives the annual consumption of hydroelectric
power (in quadrillion BTU) in the United States
for selected years since 1983. From Table 2 it appears that
a polynomial model of the data would have three turning
points—near 1989, 1997, and 2001. Because a polynomial
with three turning points must have degree at least four,
we can model the data with a quartic (fourth-degree)
polynomial:
y 0.00013x 4 0.0067x 3 0.107x 2 0.59x 4.03
where y is the consumption (in quadrillion BTU) and x is time in years with x 0 representing
1983.
(A) Use the model to predict the consumption of hydroelectric power in 2018.
(B) Compare the consumption of hydroelectric power in 2003 (as given by Table 2) to the
consumption given by the model.
(A) If x 35 (which represents the year 2018), then
y 0.00013(35) 4 0.0067(35) 3 0.107(35) 2 0.59(35) 4.03 22.3
The model predicts a consumption of 22.3 quadrillion BTU in 2018. However,
because the predicted consumption for 2018 is so dramatically greater than earlier
consumption levels, it is unlikely to be accurate. This brings up an important point: A
model that fits a set of data points well is not automatically a good model for
predicting future trends.